For various reasons, the diophantine equation 15a + b = 2^2000 has the solutions
a = 2^2000 + 2^2000 * t,
b = -14*2^2000 - 15*2^2000 * t,
where t is some integer. Now, if x^2 = a and y^2 = b (with x, y natural), then it's necessary (but obviously not sufficient) that both a and b be positive. This places some severe restrictions on t, in fact, if you try to solve the system
a >= 0
b >= 0
you'll find that t = -1 is the only possibility, but then a = 0, which isn't odd.
Damn it, it should be a = 2^2000 + t, b = -14*2^2000 - 15t... I messed up trying to distribute a multiplication over a parenthesis. This breaks the "solution". :(
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